OMK 2009 Results

November 7, 2009 1 comment

For your information, the official result for the Olimpiad Matematik Kebangsaan 2009 has been announced.

You can check your results here, and for its related article, here.

Categories: Announcement Tags: ,

Multiple-choice question …

October 1, 2009 1 comment

Answer & Solution – click here

Categories: Puzzles Tags:

Another short quiz.

September 30, 2009 Leave a comment

Show that
\sum_{i=1}^k \frac{k-i}{\sqrt{i}+\sqrt{i+1}}=\sqrt{1}+\sqrt{2}+\sqrt{3}+\dots+\sqrt{k-1}+\sqrt{k} .
Hence, proof
\sum_{i=1}^k \frac{k-i}{\sqrt{i}+\sqrt{i+1}}\leq k \sqrt{\frac{k+1}{2}}.
Note: The second part is actually a practice of the Cauchy-Schwarz inequality, which in general, for a_n , b_n \, \in \textbf{R} \, \text{for} \, 1 \leq n \leq i :
\left({a_1}^2+{a_2}^2+\dots+{a_i}^2\right)\left({b_1}^2+{b_2}^2+\dots+{b_i}^2\right)\geq \left(a_1 b_1 + a_2 b_2 +\dots + a_i b_i\right)^2

Categories: Problems Tags: , ,

Short Quiz

September 29, 2009 8 comments

1. Find \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\dots}}}}}.
2. Simplify \frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\dots+\frac{1}{\sqrt{2001}+\sqrt{2002}}+\frac{1}{\sqrt{2002}+\sqrt{2003}}.

Categories: Problems Tags: ,

Instructions for OMK Participants

June 16, 2009 Leave a comment

Please refer to the file below for the official instructions for OMK participants.

And do prepare well for the upcoming OMK this Saturday (and sleep well)

Good luck !

Arahan kepada Calon OMK.

Categories: Announcement Tags:

OMK Actual Problem (2007)

June 16, 2009 Leave a comment

You may download the file below, which is the actual question for OMK 2007 released by PERSAMA along with the answers and marking scheme. Those who are interested, you may download it, and try the questions accroding to your category. For those who would like to try the previous selection tests done in the school, you may refer to the website’s archive/ previous posts.

Soalan-Jawapan_OMK-2007

Categories: Problems Tags:

Training Problems

June 5, 2009 5 comments

Please download the file below as a set of training problems for the upcoming OMK.
Training Problems

Categories: Problems Tags: ,

OMK Selection Test 2009 – Bon.gsu Category Solution

April 15, 2009 2 comments

The solution for the Bon.gsu paper has completed. You may download it here:
su-2009-solution1

Categories: Solutions Tags: , ,

Announcement

April 14, 2009 Leave a comment

For those who are under Muda and Sulong Category, if you didn’t score well in the previous selection test, do not worry.

There will another test coming soon, and we will finalize the OMK team after the test.

I would probably set the paper similiar to Hua Lo-Keng Cup, which is in multiple-choice, with an additional choice of selecting “No answer” or “Cannot be determined using given information”. A penalty system will also be applied to the scoring for incorrect attempt. However, I will also include some structure question, but not many, don’t worry.

Before that,  please try the posted problems and understand the solution. Good Luck !

Categories: Announcement Tags:

OMK Selection Test 2009 Bon.gsu Category Official Result

April 14, 2009 Leave a comment

Another set of results released for the Bon.gsu Category:

su-2009-results

The complete solution for the question will be posted soon, so please wait patiently.

Categories: Announcement Tags: , ,
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